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Math Help - progression equation

  1. #1
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    Question progression equation

    Hi Friends,

    Case A:

    1, 3, 5, 7, 9.....
    To find the Nth term for the above type of progression, the equation is:
    Nth term = a + (n-1)d
    where a = initial term
    d = common difference
    n = number of terms


    Case B:

    1, 2, 4, 7, 11, ....

    My question is: Is there any general equation to find the Nth term for the above type of progression ?
    Note that the common difference is variable but has a constant progressive rate i.e, 1,2,3,4,.... and iteself has a common difference of 1


    Thanks in advance.
    Regards.
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  2. #2
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    Re: progression equation

    Case B: yes.

    Note that

    a_1 = 1
    a_2 = 1+1
    a_3 = 1+1+2
    a_4 = 1+1+2+3
    a_n = 1+(1+2+...+(n-1))

    Therefore, a_n = 1 + (1+2+...+(n-1)) = 1+\frac{(n-1)n}{2}
    Last edited by richard1234; June 16th 2012 at 10:24 PM.
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  3. #3
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    Thumbs up Re: progression equation

    Thank you very much richard1234.
    That's perfect. Have a nice day.
    Last edited by bytelogik; June 16th 2012 at 11:15 PM. Reason: Solved
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